Several interesting features concerning the reflection of obliquely incident electromagnetic waves from a dielectric half‐space moving at relativistic velocities are discussed. Two cases of the movement are considered: (a) The dielectric medium moves parallel to the interface. (b) The dielectric medium moves perpendicular to the interface. Both polarizations of the incident wave are considered: (a) The electric field of the incident wave lies in plane of incidence. (b) The electric field of the incident wave lies in a plane which is normal to the plane of incidence. The variation of the Brewster angle as a function of the velocity of the medium is examined in particular. Also considered in detail are the energy relations of this moving boundary problem.